Only a quarter of older people would consider voting Labour at another election, according to a new survey that highlights the challenge faced by Jeremy Corbyn in winning over the “grey vote”.

Just 26% of voters aged 65 to 74 say Labour would be an option for them if another election was called. Crucially, this includes the 25% who voted for Corbyn’s party at the June general election, suggesting Labour has only a tiny number of potential new recruits among this age group.

As Labour activists gather in buoyant mood for their annual conference in Brighton this weekend, the polling by Opinium for the Social Market Foundation shows the party’s current popularity is heavily concentrated among younger age groups who continue to be attracted by its messages. However, support shows little sign of expanding among pensioners.

Among 18- to 24-year-olds, 63% said they would consider voting Labour – substantially more than the 53% who chose the party in the snap June election, suggesting it continues to build appeal among young people. Among 25- to 34-year-olds the same proportion (63%) said they would think about Labour, compared with the 49% who chose them at the last election.

The party’s lack of appeal among older voters – who turn out in larger numbers at the ballot box than younger ones – is worrying party strategists. They realise that unless Corbyn and his team can appeal more to older sections of the electorate the party will struggle to supplant the Tories, even if Theresa May’s government implodes.

Concern about Labour’s lack of economic credibility as well as worries about its attitude to defence are often cited by older voters as reasons for not backing the Labour.

In June, the Tories won more seats than Labour at the general election because they outpolled Corbyn’s party by more than two to one among older voters.

Opinium found that only 30% of people aged over 65 said they believed Labour was on the side of “people like me”. By contrast, 54% said they regarded Labour as the party of young people. This is despite the fact that Labour went out of its way to try to lure older voters in its last election campaign with pledges to maintain pensioner benefits such as winter fuel payments and the “triple lock” on pensions.

The data, to be revealed by Social Market Foundation at a fringe event at the conference on Monday, suggests the best way for Labour to widen its appeal would be to offer credible tax, spending and other economic policies. Almost half of older voters said they would consider supporting the party if they believed it could be trusted to manage the public finances.

Adam Drummond of Opinium said: “Their best chance of making any gains with older voters lies in making the party a safe choice for those who would like to kick out the incumbent government but are more worried about the opposition.”

An eve of conference poll by Opinium for the Observer puts the Tories two points ahead of Labour. The Conservatives are on 42%, Labour on 40%, the Lib Dems on 6% and Ukip and the SNP both on 4%.

Corbyn is still just ahead of May in the net personal ratings (when the number of those who disapprove of his leadership are subtracted from those who approve). But his rating has slipped from –5 to –10% over the last month.

May is now on minus 11% but has improved her rating by six points since last month when she was on minus 17%.